Funny thing, this... When I was young and starting out, for the first 5 years, in fact. I played with a "wet" (saliva moistened embouchure).
Howbeit, as I aged, and (according to myself) improved I played dry. I no longer had to position the mouthpiece for highs and lows as previously. I discovered I could keep the mouthpiece in one position for all playing. And so it remains.